Structure-Property Relations

242 Pages·1975·8.09 MB·English

by  Professor Robert E. Newnham (auth.)

Crystal Chemistry
of N on- Metallic Materials
2
Robert E. Newnham
St ructure-Property
Relations
With 92 Figures
Springer-Verlag Berlin Heidelberg New York 1975
Professor Rohert E. N ewnham
Materials Research Laboratory
The Pennsylvania State University
University Park, PA 16802/USA
ISBN 978-3-642-50019-0 ISBN 978-3-642-50017-6 (eBook)
DOI 10.1007/978-3 -642-50017-6
This work is subject to copyright. An fights are reserved, whether the whole or part of the material is concerned,
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Of similar means. and storage in data banks.
Under § 54 of tbe German Copyright Law where copies are made rar other than private use, a fee is payable to
the publisher, the amaunt ofthe fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin· Heidelberg 1975.
Library of Congress Cataloging in Publication Data. Newnham. Robert Everest. 1929-. Structure-property relations.
(Crystal chemistry of non-metallic materials; 2). Ineludes bibliographical references and index. 1. Crystals. 2. Nonmetallic
materials. I. Title. 11. Serie,. QD931.N48. 548'.8. 75·14174.
The use of registered names, trademarks, ete. in this publication does not imply, even in the absence of a specifie
statement, that such names are exempt from the relevant proteetive laws and regulations and therefore free for general
use.
Preface
As a boy I loved to build model airplanes, not the snap-together
plastic models of today, but the old-fashioned Spads and Sopwith
Camels made of balsa wood and tissue paper. I dreamed of EDDIE
RICKENBACKER and dogfights with the Red Baron as I sat there sniffing
airplane glue. Mother thought I would never grow up to make an honest
living, and mothers are never wrong. Thirty years later I sit in a research
laboratory surrounded by crystal models and dream of what it would
be like to be 1 A tall, to rearrange atoms with pick and shovel, and
make funny things happen inside. Professor VON HIPPEL calls it
"Molecular Engineering," the building of materials and devices to order:
We begin to design materials with prescribed properties, to under
stand the molecular causes of their failings, to build into them safe
guards against such failure, and to arrive at true yardsticks of
ultimate performance. No longer shackled to presently available
materials, we are free to dream and find answers to unprecedented
challenges. It is this revolutionary situation which makes scientists
and engineers true allies in a great adventure of the human mind [1].
This book is about structure-property relationships, more especially
applications of crystal chemistry to engineering problems. Faced with
the task of finding new materials, the crystallographer uses ionic radii,
crystal fields, anisotropic atomic groupings, and symmetry arguments
as criteria in the materials selection process. Symmetry is reviewed in
the first chapter, emphasizing its influence on physical properties. In
general, symmetry is helpful in determining which effects are absent, but
not in estimating the relative sizes of property coefficients. Magnitudes
depend more on the atomistic arguments presented in later chapters.
Using illustrations from present day technology, I have tried to point
out the crystallochemical parameters most important to the under
standing of molecular mechanisms, and to the choice of new materials.
WILLIAM SHOCKLEY, co-inventor of the transistor, has said it much
better [2]. The modus operandi of research programs is to seek
fundamental understanding while at the same time remaining alert for
possible applications. For many solid state problems, it is helpful to ask,
What are the atoms involved and how are they arranged?
How did this arrangement come into being?
VI Preface
How does this arrangement lead to certain mechanisms of electronic
and atomic motion?
How do these mechanisms give rise to the observed properties?
Those are the questions I had in mind when I wrote this book, but
in looking over the result, I have a sad feeling that it falls far short of
the mark. As the Pennsylvania Dutch say, "Ve grow too soon oldt, undt
too late schmart."
The preparation of a book requires support in many ways. Looking
back, I would like to thank ETHEL CALLAHAN, LOUIS WEBER, RAY
PEPINSKY, GEORGE BRINDLEY, HELEN MEGAW, and ARTHUR VON HIPPEL
for helping me on my way. There are too many wonderful colleagues
here at Penn State to acknowledge each individually, but I want to give
special thanks to ERIC CROSS, the originator of most of "my" best ideas.
The book would still be submerged among the lunch bags on my desk
were it not for the efforts of DOYLE SKINNER, DICK HORSEY, DARIA
SESSAMEN, and RUSTUM RoY, the editor of this series. No man is an
island-to coin a phrase-and no man has a finer family than mine:
Pat, Randy, Rosie, Mom and Dad are wonderful to live with, and except
for Zoomer, none are the least big grouchy. Every day is a happy one.
University Park, February 1975 ROBERT NEWNHAM
References
1. VON HIPPEL, A.: Science 138, 91 (1962).
2. SHOCKLEY,W.: Electrons and holes in semiconductors. New York: D. Van
Nostrand Co. 1950.
Contents
I. Symmetry and Crystal Physics. 1
1. Crystal Classes .... . 2
2. Space Groups .... . 5
3. Symmetry Distribution of Crystals 8
4. Bond Length Calculations 10
5. Density ......... . 11
6. Physical Properties . . . . . . 12
7. Symmetry of Physical Properties 14
8. Tensors ..... 16
9. Magnetic Symmetry 19
References for Chapter I 23
II. Electronic Transport in Materials . . . . . . . . . . . . 24
1. Atomic Orbitals, Molecular Orbitals, and Energy Bands 24
2. Electronic Materials . . 30
3. Semiconductors 32
4. Band Gap and Mobility 35
5. Semiconductor Doping 37
6. Semimetals and Narrow Gap Semiconductors 40
7. Magnetic Semiconductors 41
8. Molecular Circuits 42
9. Metal-Metal Bonding 43
10. Anisotropic Conductors 44
11. Superconductivity 45
References for Chapter II 51
III. Thermal Properties and Ion Transport 52
1. Lattice Vibrations . . 53
2. Thermal Properties 55
3. Thermal Conductivity 57
VIII Contents
4. Ultrasonic Attenuation 59
5. Thermal Expansion 60
6. Diffusion 64
7. Ionic Conductivity 68
8. Ionic Switches 70
9. Superionic Conductors 71
10. Solid State Battery Materials 73
11. Photographic Process 74
12. Thermoelectric Materials 75
13. Thermionic Materials 75
References for Chapter III 76
IV. Ferroelectrics and Other Ferroic Materials 78
1. Polar Crystals and Pyroelectricity 79
2. Piezoelectricity 82
3. Acoustoelectric Effect 85
4. F erroelectricit y 86
5. Hydrogen-Bonded Ferroelectrics 89
6. Classification of Ferroelectrics 91
7. Transition-Temperature and Coercive Field 92
8. Ferroic Crystals 94
9. Free Energy Formulation 96
10. Primary Ferroic Minerals 98
11. Secondary Ferroics 104
12. Ferroic Symmetry Species 111
References for Chapter IV 113
V. Optical Materials 115
1. Luster 117
2. Birefringence and Crystal Structure 118
3. Optical Windows 121
4. Color 123
5. Crystalline Lasers 126
6. Semiconductor Lamps 128
7. Luminescence 129
8. Cathodochromic and Photochromic Materials 133
9. Optical Activity 135
10. Photoelasticity 138
11. Nonlinear Optical Materials 140
References for Chapter V 143
Contents IX
VI. Magnetic Materials 144
1. Diamagnetism .... 145
2. Transition-Metal Atoms 146
3. Crystal Field Theory 148
4. Paramagnetic Salts 152
5. Transition Temperatures 153
6. Magnetization 155
7. Crystalline Anisotropy 157
8. Hard and Soft Magnets 160
9. Bubble Memories . . 162
10. Microwave Garnets 166
11. Magnetooptic Materials 168
12. Magnetoelectricity 170
References for Chapter VI 171
VII. Materials with Useful Mechanical Properties 173
1. Elasticity .... 173
2. Mechanical Analog 175
3. Elastic Anisotropy 180
4. Pressure Dependence of the Elastic Stiffness 188
5. Temperature Dependence of the Elastic Stiffness 190
6. Temperature-Compensated Materials .... 191
7. Surface Wave Materials .......... 195
8. Molecular Geometry and Molecular Flexibility 196
9. Hardness ..... 198
10. Grinding and Polishing ...... . 200
11. Friction and Wear . . . . . . . 203
12. Dislocations and Plastic Deformation . 205
13. Hard Metals . 210
14. Cleavage . 211
15. Brittle Fracture . 213
16. Toughness . . . 214
17. Strengthening of Glass . 217
18. Composite Materials 218
References for Chapter VII . 220
Chemical Index . 223
Subject Index . . 229
1. Symmetry and Crystal Physics
All crystals have translational periodicity and most possess other
symmetry elements as well. A symmetry operation relates one part of an
object to another. After performing the symmetry operation, the object
is indistinguishable from its original appearance, both in form and
orientation. We live in a three-dimensional world *, and as a con
sequence there are three principal types of symmetry operators: two
dimensional mirror planes, one-dimensional rotation axes, and zero
dimensional inversion centers. Consider a set of orthogonal axes X, Y, z.
A mirror plane at Y = 0 takes any point at (x, y, z) and transforms it to
(x, - y, z), changing the sign of the y-coordinate. The mirror plane is a
symmetry element of the object if it appears identical, before and after
the mirror operator is applied. Two-fold rotation axes occur in many
crystals. If the axis is coincident with Z, then a point at (x, y, z) is rotated
1800 about Z to ( - x, - y, z), changing the sign of two of the coordinates.
An inversion center at the origin of the coordinate system transforms
(x, y, z) to ( - x, - y, - z). The three symmetry operations are illustrated
in Fig. I.
,4r----------------------y
I
f<
(bl~
(0) (c)
._ <:~i::::::::::::::::::::: ::)
Fig. la-c. Crystals illustrating the three principal types of symmetry elements:
inversion, reflection and rotation. Chalcanthite (CuS04· 5 H20), (a) crystals show
a center of symmetry only, while hilgardite (CaBBIB033C14· 4H 0), (b) has mirror
2
--_sym.m etry, and sucrose (C12H220 Il), (c) has a single two-fold rotation axis
* The reason why our world has three space dimensions was discussed at a
recent meeting of the American Physical Society [1]. It can be proved that for
dimensionality n = 3, and only for n = 3, any ordered sequence of n-dimensional
hypersurfaces with given intrinsic geometries and with given normal separations
becomes, in the limit of infinitesimal separations, an (n + I)-dimensional manifold
with a unique metric. For n ~ 3, any such ordered sequence becomes in the limit
an (n + I)-dimensional manifold with metric-but when n < 3 the resulting metric
is not unique. Furthermore, n ~ 3, every sequence, which becomes in the limit an
(n + 1)-dimensional manifold with metric, has a unique metric; but for n> 3, some
sequences do not become a manifold with metric at all.
2 1. Symmetry and Crystal Physics
1. Crystal Classes
A point group is a self-consistent set of symmetry elements operating
around a point. There are an infinite number of point groups, but only
thirty-two are consistent with the translational periodicity found in
crystals. The thirty-two crystal classes govern the physical properties
of crystals.
Hermann-Mauguin symbols are used in describing symmetry ele
ments and point groups. Numbers denote rotation axes: a three-fold
symmetry axis with rotation of 360°/3 = 120° is simply 3. A mirror plane
is m and its orientation can be inferred from the point group symbol.
s' s"
_--:..:.m:...;t'----_
Fig. 2. A one-dimensional chain with rotation axes normal to the paper. The only
allowed values of <P are those corresponding to 1-, 2-, 3-, 4-, and 6-fold
symmetry axes
3/m means the three-fold axis is perpendicular to the mirror plane. In
class 3 m, the three-fold axis lies in the mirror plane. Inversion symmetry
does not appear explicitly as a symbol, though many of the groups are
centric. The reason for this is that the symbol lists only the independent
symmetry elements. As an example, consider the monoclinic class 2/m
which contains a two-fold axis along Y, a mirror plane perpendicular to
Y, and a center of symmetry at the origin. The two-fold axis carries a
point (x, y, z) to ( - x, y, - z). Operating on ( - x, y, - z) with the mirror
plane takes it to ( - x, - y, - z). Thus consecutive operations of 2 and m
take the point from (x, y, z) to ( - x, - y, - z), the same as the inversion
operation.
The thirty-two crystal classes can be derived geometrically by answer
ing the following questions. Which types of rotational symmetry are
consistent with translational periodicity? Which combinations of inter
secting rotation axes are possible? How are the various types of
rotational symmetry combined with mirror and inversion symmetry?
Using Fig. 2, it is easy to show that only five types of rotational
symmetry are consistent with translation. Imagine a one-dimensional